Zero path length difference

Figure 4.10 (Top) Schematic diagram of a Michelson interferometer. ZPD stands for zero path-length difference (i.e., the fixed mirror and moving mirror are equidistant from the heamsplitter). (From Coates, used with permission). (Bottom) A simple commercial FTIR spectrometer layout showing the He-Ne laser, optics, the source, as well as the source, interferometer, sample, and detector. [Courtesy of ThermoNicolet, Madison, WI (www.thermonicolet.com).]...

Evaluating these integrals involves the determination of the values at zero path length and at very long, or infinite, path length. At zero path length difference... 

Fig. 40.2. Interference of two beams with the same frequency (wavelength). The path-length difference between beams (a) and (b) is zero, between (a) and (c) X/2, between (a) and (d) A/5 (a+b), (a+c) and (a+d) are the amplitudes after recombination of the beams.

The path length difference is thus zero for 9 = 0 and increases with increasing 9 (Figure 9-7). The ratio z of the scattering intensity at two dif-... 

Two techniques are useful for locating the zero path difference position of the mirrors. One of these is to use a monochromatic light source and locate that position of the two mirrors for which the central fringe has expanded to fill the field of view as mentioned above. Another is to use a monochromatic light source that is actually a doublet such as the sodium D line. The interference produced by two closely spaced spectral lines will be a sine wave whose amplitude varies at some lower sinusoidal frequency. The output of the interferometer is focused on a photomultiplier and the path length difference of the two mirrors is varied in some uniform manner (i,e. a sawtooth motion). 

The detailed action at the beam splitter is complex, but as shown in Fig. 2.4(d), when the two mirrors are equidistant from the beam splitter, constructive interference occurs for the beam going to the detector, and destructive interference occurs for the beam going back to the source, for all wavelengths of radiation. The path length of the two beams in the interferometer are equal in this case, and the path length difference, called the retardation, is zero. 

Since the left side of Eq. (7) represents the release rat of the system, a true controlled-release system with a zero-order release rate can be possible only if all of the variables on the right side of Eq. (7) remain constant. A constant effective area of diffusion, diffusional path length, concentration difference, and diffusion coefficient are required to obtain a release rate that is constant. These systems often fail to deliver at a constant rate, since it is especially difficult to maintain all these... 

Consider the same unit cell, under the same conditions, in Figure 5.12b. If an atom lay exactly on an hkl plane, then the phase of the wave scattered by that atom would be zero with respect to the plane. Remember that all points on a plane scatter with identical phases (see above). Because there is one wavelength difference in the path length for waves scattered by successive planes in the family when Bragg s law is satisfied, atoms lying exactly on other planes would also scatter with a phase of 0 = 0 + 2jt = 0 + nn = 0. 

The optical path difference (OPD) between the beams that travel to the fixed and movable mirror and back to the beamsplitter is called retardation, 8. When the path length on both arms of the interferometer are equal, the position of the moving mirrors is referred to as the position of zero retardation or zero path difference (ZPD). The two beams are perfectly in phase on recombination at the beamsplitter, where the beams interfere constructively and the intensity of the beam passing to the detector is the sum of the intensities of the beams passing to the fixed and movable mirrors. Therefore, all the light from the source reaches the detector at this point and none returns to the source. To understand why no radiation returns to the source at ZPD one has to consider the phases on the beam splitter. 

Another simple case is a homogeneously growing single-phase layer, which allows only a slow diffusional transport of corrosive medium to the substrate. Here the steady state means for Eq. (5) that a layer, and hence the diffusion path length /, is growing with time while the absolute concentration difference Ac stays constant. At the substrate-oxide interface, the equilibrium with the material is achieved or the concentration of the agent can be approximated to zero, while the concentration at the surface of the scale is constant at the solubility limit of the scale material. 

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